I Murray Gell-Mann on Entanglement

[secur]

... it's the minimal approach ...

Right. Not the minimal ensemble approach. Having dropped that unnecessary and misleading term, your approach becomes just shut up and calculate. No one can argue with that.

 

[secur]

I agree with Gell-Mann ... So the physicist is always agnostic about causation until it is demonstrated as such ...

You're right. the physicist is - should be - agnostic on this and similar issues. At this time we don't know if there's any causation in the Bell experiment. There's no point in talking about it, until some new data is available.

But Gell-Mann said: "People say loosely ,crudely, wrongly that when you measure one of the photons it does something to the other one. It doesn't."

He's not agnostic. He's strongly denying any causative link. Neither of us can agree with that statement.

BTW it doesn't matter what he did or didn't say, and whether we agree - except, after all, that's what the OP asked.

 

[Ken G]

Right. Not the minimal ensemble approach. Having dropped that unnecessary and misleading term, your approach becomes just shut up and calculate. No one can argue with that.

I don't actually like "shut up and calculate", because it suggests that all that matters is the outcome of the calculation. I think more than that matters, that the scientist must always keep careful track of what they are testing and what they are simply assuming. It's OK to make assumptions, but they go in a different box from what has been demonstrated by testing. So there is an important philosophical component, but it is the philosophy of scientific thinking.

 

[Ken G]

But Gell-Mann said: "People say loosely ,crudely, wrongly that when you measure one of the photons it does something to the other one. It doesn't."

Yes, you're right that Gell-Mann is going beyond agnosticism. I should have said I would have agreed with him had he simply said "people say that when you measure one of the photons it does something to the other, but in fact we have no need to imagine that is true, and no scientific evidence that it is true."

 

[ShayanJ]

Collapse is needed for the consistency of quantum mechanics (in the Schroedinger picture).

If you do calculations in one frame in which collapse is not needed, the collapse will be needed to achieve the same prediction in a different frame, assuming you use the Schroedinger picture.

So collapse preserves the principle of relativity: any frame is as good as any other.

But vanhees's description is frame independent and it doesn't need collapse. So I'm confused by your statement!
What criteria should a frame meet so that we don't need collapse to explain Bell type experiments in it?

 

[atyy]

But vanhees's description is frame independent and it doesn't need collapse. So I'm confused by your statement!
What criteria should a frame meet so that we don't need collapse to explain Bell type experiments in it?

In my understanding, for a Bell test, since the measurements are at spacelike separation, there is one frame in which A and B measure simultaneously. Since there is only one measurement in that frame, collapse is not required in that frame.

By relativity of simultaneity, if A and B measure simultaneously in one frame, they must measure sequentially in another frame. Thus in another frame one would have A measuring first, followed by B measuring. In that frame, the collapse is needed to specify the state of the system after A has measured.

 

[ShayanJ]

In my understanding, for a Bell test, since the measurements are at spacelike separation, there is one frame in which A and B measure simultaneously. Since there is only one measurement in that frame, collapse is not required in that frame.

By relativity of simultaneity, if A and B measure simultaneously in one frame, they must measure sequentially in another frame. Thus in another frame one would have A measuring first, followed by B measuring. In that frame, the collapse is needed to specify the state of the system after A has measured.

That makes sense for QFT. But that means NRQM doesn't need collapse because Galilean transformations preserve simultaneity of the experiments.

 

[atyy]

That makes sense for QFT. But that means NRQM doesn't need collapse because Galilean transformations preserve simultaneity of the experiments.

If you perform sequential measurements in NRQM, and use the Schroedinger picture, you will still need collapse.

 

[ddd123]

The reason I agree with Gell-Mann is that I feel in physics we should have a standard for the word "effect" that is different from what a philosopher might use. To say we have an "effect", we must be able to demonstrate causation, not merely correlation. Entanglement is an example of the old adage "correlation is not causation", because causation requires an arrow that is not present in a correlation. So the physicist is always agnostic about causation until it is demonstrated as such-- it is never necessary to demonstrate the absence of causation, it is necessary to demonstrate its presence by means that go beyond correlation.

How do you prove that there is causation?

 

[ShayanJ]

If you perform sequential measurements in NRQM, and use the Schroedinger picture, you will still need collapse.

If collapse is actually in the theory, its existence shouldn't depend on what picture we use. So if collapse is there in the Schrodinger picture, it should have a counterpart in the Heisenberg picture, some kind of an evolution for operators that doesn't satisfy the Heisenberg's equation of motion. Otherwise we can just stop using Schrodinger picture and then there is no collapse in the theory!

But otherwise, what you say makes sense to me!

 

[atyy]

If collapse is actually in the theory, its existence shouldn't depend on what picture we use. So if collapse is there in the Schrodinger picture, it should have a counterpart in the Heisenberg picture, some kind of an evolution for operators that doesn't satisfy the Heisenberg's equation of motion. Otherwise we can just stop using Schrodinger picture and then there is no collapse in the theory!

But otherwise, what you say makes sense to me!

Yes, you can hide the collapse by going in a sophisticated way to the Heisenberg picture - this requires a generalization of the Born rule. I have no problem with that.

There are other ways to avoid collapse, like insisting on never making sequential measurements (in principle it is possible, but almost impossible in practice).

Similarly, Bob can avoid nonlocality by insisting that Alice is not real at spacelike separation.

Many choices are possible, including accepting that the locality can be derived from nonlocality - concretely, the reduced density matrix of B (showing locality) is derived by tracing over the collapsed wave function of both A and B (showing nonlocality).

 

[ShayanJ]

this requires a generalization of the Born rule

Can you provide a reference?

 

[atyy]

Can you provide a reference?

This is not the most general form, but it will give you the right idea: Eq 37 of http://arxiv.org/abs/quant-ph/0209123.

 

[Ken G]

How do you prove that there is causation?

The scientist never proves anything, they use models successfully. Causation is something that we say is present when we find that by using that concept, it gives us power over the situation. We control one thing, in order to control something else-- that's the value of the causation concept. But like all our concepts, we tend to take them too literally, and try to apply them in situations where we gain nothing by doing so. Like entanglement.

 

[vanhees71]

The collapse is nonlocal in the sense that the wave function is assigned to a spacelike surface of simultaneity, and the wavefunction on that hypersurface collapses instantaneously.

From the nonlocal collapse, the reduced density matrix of B can be derived, from which it can be seen that the collapse does not allow superluminal signalling.

So locality can be derived from nonlocality, and nonlocality does not contradict locality.

I disagree, and that's also not in accordance with what Peres writes in the here discussed article. Again, you have to distinguish between longranged-correlations ("nonlocality" realized by entanglement also in relativistic QFT) and local interactions (realized by microcausality of the local observables and locality of the interaction Hamiltonian, as also clearly specified by Peres; he gives even a stronger argument, why relativistic QT should be realized as local relativistic QFT, then Weinberg in QT of Fields vol. I!).

 

[vanhees71]

That makes sense for QFT. But that means NRQM doesn't need collapse because Galilean transformations preserve simultaneity of the experiments.

In other words: Nothing is wrong with even a naive collapse assumption for non-relativistic QT. There you can use it without contradicting the theory itself. That's not possible for relativistic local QFT (as applied in the formulation of the Standard Model). There a naive collapse assumption contradicts the very foundations of the theory. Since NRQT is just an approximation of relativistic QFT, one shouldn't use the collapse assumption there either, but at least it's not self-contradictory as if applied for relativistic QFT.

 

[vanhees71]

This is not the most general form, but it will give you the right idea: Eq 37 of http://arxiv.org/abs/quant-ph/0209123.

Why do you say there is an extension of the Born rule? Also note that the outcome of anything physical like the said probabilities are independent of the picture of time evolution since any two pictures of time evolution are connected by unitary transformations. It may be more or less convenient to use a specific picture, but there cannot be any difference concerning the physical outcomes of the formalism due to the change of the picture.

 

[Weddgyr]

"People say loosely ,crudely,wrongly that when you measure one of the photons it does something to the other one. It doesn't."
Do most physicists working in this field agree with the above statement ?

Most physicists are trained to avoid asking the question. It's been a hugely successful program.

There aren't any answers as of today. You can assume a non-local influence if you like, but that will be philosophically in conflict with relativity, etc. You can assume a conspiracy/super-determinism of detector settings, etc, which will be another philosophical muddle. You can just accept the quantum correlations as is, without need for a causal mechanism, but you will then be in conflict with the general philosophy of the scientific method. Above all you are a physicist so whichever option you pick you will of course NOT be doing any of that philosophical crap.

 

[Simon Phoenix]

That's not possible for relativistic local QFT (as applied in the formulation of the Standard Model). There a naive collapse assumption contradicts the very foundations of the theory

OK - that's fair enough - but does assuming a naïve collapse model actually lead one to derive any inconsistent experimental results?

 

[ShayanJ]

In other words: Nothing is wrong with even a naive collapse assumption for non-relativistic QT. There you can use it without contradicting the theory itself. That's not possible for relativistic local QFT (as applied in the formulation of the Standard Model). There a naive collapse assumption contradicts the very foundations of the theory. Since NRQT is just an approximation of relativistic QFT, one shouldn't use the collapse assumption there either, but at least it's not self-contradictory as if applied for relativistic QFT.

I'm trying to make sense of the way you think about this. But I seem to lack some essential knowledge about how people like you actually use QM.
The part I know is that you prepare a large number of identical systems in identical quantum states. Of course the preparation device is not perfect and there may be some deviations from the desired state, but I don't know whether you take that into account and use a mixed state for the ensemble or just make the approximation of a perfect device and use the desired pure state.
Anyway, the next step is you measure the probability distribution of a desired observable on this ensemble. What I don't understand is, what do you do if you want to measure the probability distribution of another observable on the same ensemble. Would you assume its in the same state before the first measurement? Or you do a Bayesian update? Is it even possible to do a second measurement on the same ensemble?

 

[vanhees71]

Maybe, I don't understand the question right, because I don't see, where there should be a problem. I just measure the observable I want. If I want to measure one observable at a time $t_1$ and then another on the same system at $t_2$ I just do so. What should I update? Of course, when predicting what's measured at $t_1$ I have to somehow describe what happens to the system due to the interaction with the measurement device at the first measurement. I also don't know what you mean by "Bayesian update". If measurement number 1 is a von Neumann filter measurement, of course I update the state in the usual sense. Also, why shouldn't it be possible to do a second measuerement on the same system within the ensemble? It depends of course what you do to the system with the 1st measurement. If I absorb the photon in the 1st measurement, of course, I cannot measure anything on this very same photon at a later time.

 

[Herman Trivilino]

That makes sense for QFT. But that means NRQM doesn't need collapse because Galilean transformations preserve simultaneity of the experiments.

But Galilean transformations are an approximation valid only when speeds are slow or separation distances between events are not very very large. It's hardly worth using it to form a worldview.

 

[stevendaryl]

OK - that's fair enough - but does assuming a naïve collapse model actually lead one to derive any inconsistent experimental results?

I would say that it doesn't. Instantaneous physical collapse is incompatible with the principles of Special Relativity, but I don't think it is incompatible with any experimental evidence.

 

[stevendaryl]

Maybe, I don't understand the question right, because I don't see, where there should be a problem. I just measure the observable I want. If I want to measure one observable at a time $t_1$ and then another on the same system at $t_2$ I just do so. What should I update?

The wave function used at time t_2. You prepare a system in state |\psi\rangle. At time t_1, the state has evolved to some new state, |\psi(t_1)\rangle = e^{-iHt_1} |\psi \rangle. At this moment, you perform a measurement of observable O and get result \lambda. Then for predictions about measurements at time t_2, you don't use |\psi(t_2)\rangle, you use |\psi'(t_2)\rangle, where |\psi'(t_2)\rangle = e^{-i H (t_2 - t_1)} \Pi_{O,\lambda} e^{-iH t_1} |\psi \rangle, where \Pi_{O,\lambda} is the projection operator that projects onto the subspace of the Hilbert space corresponding to eigenvalue \lambda of operator O. So the "update" being discussed is switching from |\psi(t_1)\rangle = e^{-iHt_1} |\psi\rangle to \Pi_{O,\lambda} |\psi(t_1)\rangle. That update is what people mean by "collapse of the wave function".

 

[vanhees71]

Sure, this describes a von Neumann Filter measurement. This update, however does not mean that there's an action at a distance with a far distant entangled part of the system I've measured.

 

[zonde]

But what is then "collapse" other than that A updates her knowledge due to the achieved polarization measurement of her photon (and the knowledge that it is polarization-entangled before her measurement)? Nothing happens to B's photon, and B still has unpolarized photons. So indeed Gell-Mann is right in his statement that nothing happens to B's photon!

How can we describe "nothing happens to B's photon" in a bit more experimentally accessible way? Would you agree to formulation that "if A has measured it's photon at different angle identical measurement of B's photon would (could) give the same result"?

 

[Ken G]

The reason I can see Gell-Mann's point is that I just don't understand why anyone would want to imagine that measuring one photon does something to the other. There can be reference frames that don't even agree which measurement happened first, nor should it matter-- you have a correlation, it's part of the system. We used to think all the information needed to predict a correlation was either "carried with" each piece of the system independently, or would involve some kind of propagating signal between the parts, but quantum mechanics gave us a well-tested formalism that says that doesn't work, instead correlations are holistic. So why not just accept that correlations are holistic? We've had so many other classical notions that we discarded, like absolute time and space or the idea that two identical preparations could not lead to different outcomes, so from whence comes the need to hang on to the old notion that all information works like attributes "carried with" pieces of a system, coupled with "influences" that propagate between the pieces? We find observationally that correlations are holistic, and a Bell state successfully encodes those holistic correlations, so why tack on some extraneous mechanism for moving those correlations around from place to place like an "influence"? The very idea that a two-photon system can be comprised of two separate photons is already a notion we should look at with suspicion (because of exchange symmetries), so why take it even farther to imagine those two dubious separate photons can do things to each other?

 

[ddd123]

The reason I can see Gell-Mann's point is that I just don't understand why anyone would want to imagine that measuring one photon does something to the other. There can be reference frames that don't even agree which measurement happened first, nor should it matter-- you have a correlation, it's part of the system. We used to think all the information needed to predict a correlation was either "carried with" each piece of the system independently, or would involve some kind of propagating signal between the parts, but quantum mechanics gave us a well-tested formalism that says that doesn't work, instead correlations are holistic. So why not just accept that correlations are holistic? We've had so many other classical notions that we discarded, like absolute time and space or the idea that two identical preparations could not lead to different outcomes, so from whence comes the need to hang on to the old notion that all information works like attributes "carried with" pieces of a system, coupled with "influences" that propagate between the pieces? We find observationally that correlations are holistic, and we have a mathematical formalism for encoding holistic correlations, so why not just accept that? The very idea that a two-photon system can be comprised of two separate photons is already a notion we should look at with suspicion, so why take it even farther to imagine those two dubious separate photons can do things to each other?

I think it is because with the other replacements for the old notions you could still form a picture of what happens inbetween preparation and measurement. Even giving up determinism let's you form a picture, because you just have a different rule for an instantaneous effect. Not having any picture and working in the blind is probably crossing a boundary for how much people are ready to give up. I mean what else could you give up after that if not predictability and thus science itself?

 

[stevendaryl]

Sure, this describes a von Neumann Filter measurement. This update, however does not mean that there's an action at a distance with a far distant entangled part of the system I've measured.

Why doesn't it? The state of the distant component has changed as a result of your measurement.

 

[stevendaryl]

The reason I can see Gell-Mann's point is that I just don't understand why anyone would want to imagine that measuring one photon does something to the other. There can be reference frames that don't even agree which measurement happened first, nor should it matter-- you have a correlation, it's part of the system. We used to think all the information needed to predict a correlation was either "carried with" each piece of the system independently, or would involve some kind of propagating signal between the parts, but quantum mechanics gave us a well-tested formalism that says that doesn't work, instead correlations are holistic.

It seems to me that "holistic" and "nonlocal" might mean the same thing, here.

 

[stevendaryl]

Why doesn't it? The state of the distant component has changed as a result of your measurement.

I understand that the "state" can be interpreted as subjective, rather than objective, but what is there to a particle, other than its state? There is nothing objective, is there? If you assume the existence of something objective (observer-independent) about a particle, and say that the quantum-mechanical state only reflects our information about this, then that's basically a hidden-variables theory, and Bell showed that such a theory has to be nonlocal. If you don't assume that there is anything objective about particles, then it seems like the question of FTL influences is moot. If the distant particle doesn't have any independent reality, then what could it mean to influence it nonlocally?

 

[vanhees71]

Why doesn't it? The state of the distant component has changed as a result of your measurement.

But that interpretation contradicts the locality of the interaction between A's photon and her polarization measurement apparatus. Also if Alice measures something else of her photon after it has passed the polarization filter, say directed to let through H-photons (which with utmost accuracy can indeed be made a v Neumann filter measurement!), all the outcomes of further measurements on her photon are described by associating the polarization state $|H \rangle$ with it. For A it's totally irrelevant what's the state of B's photon, as is for B whatever A does with her photon. The correlations due to the entanglement, which itself is due to the production of the entangled photon pair in the very beginning, can, however be observed by comparing the measurement protocols with accurate timestamps of each single-photon detection event by A and B. From this point of view (the minimal statistical interpretation) there is not need for assuming a collapse at all, and that prevents this interpretation from leading to inconsistency with the very foundations of relativistic QFT!

 

[stevendaryl]

But that interpretation contradicts the locality of the interaction between A's photon and her polarization measurement apparatus.

If you posit, as Von Neumann did, the existence of two kinds of processes: (1) evolution according to Schrodinger's equation (or the equivalent for QFT), and (2) measurements, then nonlocality of the second type doesn't contradict locality for the first type. Of course, that's unsatisfying, because measurements (or observations) surely must be explainable in terms of the quantum mechanics of macroscopic devices, but it seems that any way of making sense of the Born probabilities involves making a distinction between macroscopic and microscopic phenomena. There are no probabilities involved in the evolution of a single electron. There are no probabilities involved in the evolution of two electrons. Probabilities only come into play in the interaction of something large enough to count as an observer, or a measuring device.

 

[zonde]

For A it's totally irrelevant what's the state of B's photon, as is for B whatever A does with her photon.

So you agree with this statement, right? - "If A has measured it's photon at different angle identical measurement of B's photon would (could) give the same result."

 

[stevendaryl]

I don't know how you can say "For A it's totally irrelevant what's the state of B's photon". If Alice knew the state of Bob's photon, then she would know the state of her own photon. So the state of Bob's photon is relevant to Alice.

 

[atyy]

I disagree, and that's also not in accordance with what Peres writes in the here discussed article. Again, you have to distinguish between longranged-correlations ("nonlocality" realized by entanglement also in relativistic QFT) and local interactions (realized by microcausality of the local observables and locality of the interaction Hamiltonian, as also clearly specified by Peres; he gives even a stronger argument, why relativistic QT should be realized as local relativistic QFT, then Weinberg in QT of Fields vol. I!).

Do you disagree with this statement: "Before Alice's measurement the state is $|hh \rangle + |vv \rangle$, and after the measurement the state collapses to $|hh \rangle$ if Alice measures her photon to be horizontal"?

It's the same as what Peres starts his abstract with: " If several interventions performed on a quantum system are localized in mutually space-like regions, they will be recorded as a sequence of “quantum jumps” in one Lorentz frame, and as a different sequence of jumps in another Lorentz frame."

Peres also says in his first sentence of the text: "Quantum measurements [1] are usually considered as quasi-instantaneous processes. In particular, they affect the wave function instantaneously throughout the entire configuration space."

The quantum jumps are obviously nonlocal. If they were local, his whole article would be trivial. It is because they are nonlocal that one has to ask whether that nonlocality can be consistent with locality. The answer is yes, nonlocality can be consistent with locality.

Furthermore Peres writes: "Returning to the Einstein-Podolsky-Rosen conundrum, we must analyze whether it actually involves a genuine quantum nonlocality. Such a claim has led some authors to suggest the possibility of superluminal communication."

Thus for Peres:
wave function collapse: fake quantum nonlocality
superluminal communication: genuine quantum nonlocality
no superluminal communication: genuine quantum locality

So fake quantum nonlocality is consistent with genuine quantum locality.

 

[vanhees71]

I don't know, what you mean by measuring A's photon at different angle. The preparation in the entangled state $|\Psi \rangle=|HV-VH \rangle$ implies that, if A's photon is found to be polarized in an angle $\phi$ (relative to direction $H$), then B's photon will be found in a state perpendicular to it.

Proof: Let $|\phi \rangle=\cos phi |H \rangle + \sin \phi |V \rangle$. Then, if A finds her photon to be polarized in this direction, she adapts her state of the two-photon system to
$$|\Psi_A' \rangle=|\phi \rangle \langle \phi | \otimes 1 |\Psi \rangle=\cos^2 \phi |HV \rangle - \sin^2 \phi |VH \rangle + \cos \phi \sin \phi (|VV \rangle -|HH \rangle) = (\cos \phi |H \rangle + \sin \phi |V \rangle) \otimes (\cos \phi |V \rangle - \sin \phi |H \rangle) .$$
As it turns out, if you consider only those B photons for which A found polarization in direction $|\phi \rangle$, then B will always find polarization in direction $\phi+\pi/2$.

Note that the necessary filtering to figure this out needs the exchange of the measurement protocols between A and B. Both A and B measure just unpolarized photons, i.e., A's photon will go through the $\phi$-polarization filter in 50% of the cases, and in these 50% of the cases B must measure his photon to be $\phi+\pi/2$ polarized. So there is a correlation between the photons but no action at a distance necessary to explain this result. The correlation is due to the preparation of the two-photon state in this entangled state and not due to A's polarization measurement on her single photon.

 

[stevendaryl]

Do you disagree with

Before Alice's measurement the state is $|hh \rangle + |vv \rangle$, and after the measurement the state collapses to $|hh \rangle$ if Alice measures her photon to be horizontal?

It's kind of hard to know what to make of the situation. The situation is this:

1. Initially, Bob's photon is unpolarized.
2. After Alice's measurement, his photon is polarized in some direction, but Bob doesn't know which.

That's a change, of sorts, but it's not a change that makes any difference for Bob. The only "state" of Bob's photon that matters for his measurements is its density matrix. The initial density matrix describes a so-called "improper" mixed state, which is obtained from the two-photon pure state by tracing over Alice's photon. The final density matrix is a proper mixed state, which is obtained by taking a weighted sum of pure-states. So Bob's photon's state went from an improper mixed state to a proper mixed state, which seems like a change, but they are both described by the identical matrix. So from that point of view, nothing has changed for Bob.

 

[stevendaryl]

I don't know, what you mean by measuring A's photon at different angle.

Just a general request about discussions here: If your comment is a direct response to a specific other comment, I would prefer that you either quote some part of the previous comment, or at least the name of the previous commenter.

 

[vanhees71]

Do you disagree with this statement: "Before Alice's measurement the state is $|hh \rangle + |vv \rangle$, and after the measurement the state collapses to $|hh \rangle$ if Alice measures her photon to be horizontal"?

Yes, I disagree with this statement. Correct is: If A's photon passes the h-polarization filter she associates the state $hh \rangle$ to the two photons. However, her measurement has no instantaneous influence on B's photon, i.e., there must not be a collapse if the interpretation should be consistent with the very construction of QED as a local relativistic QFT, and you don't need it!

It's the same as what Peres starts his abstract with: " If several interventions performed on a quantum system are localized in mutually space-like regions, they will be recorded as a sequence of “quantum jumps” in one Lorentz frame, and as a different sequence of jumps in another Lorentz frame."

Well, I'm also against the use of the word quantum jumps, but I guess Peres has the right thing in mind when he states this, and he is right that the temporal sequence for space-like separated "interventions" is frame dependent, which implies that one intervention cannot have a causal influence on the other space-like separated intervention. That's the whole point of our disagreement. In my (and if I understand him right also Peres's) notion of the state as epistemic (particularly the "update" or if you wish to call it with another unsharp word "quantum jump" of the state after a "filtering intervention" as in our example here) there is no tension between causality and relativistic QFT whatsoever, and that's so by construction of the QFT, and Peres's argument in the paper is just another very convincing argument for why (at least) the Hamilton density operator has to commute at spacelike separation of the arguments, i.e., if $(x-y) \cdot (x-y)<0$ (west-coast convention of the metric) you must have $[\hat{\mathcal{H}}(x),\hat{\mathcal{H}}(y)]=0$. Usually one assumes even more, i.e., that any two local operators commute at spacelike separation of their arguments.

 

[atyy]

Yes, I disagree with this statement. Correct is: If A's photon passes the h-polarization filter she associates the state $hh \rangle$ to the two photons. However, her measurement has no instantaneous influence on B's photon, i.e., there must not be a collapse if the interpretation should be consistent with the very construction of QED as a local relativistic QFT, and you don't need it!Well, I'm also against the use of the word quantum jumps, but I guess Peres has the right thing in mind when he states this, and he is right that the temporal sequence for space-like separated "interventions" is frame dependent, which implies that one intervention cannot have a causal influence on the other space-like separated intervention. That's the whole point of our disagreement. In my (and if I understand him right also Peres's) notion of the state as epistemic (particularly the "update" or if you wish to call it with another unsharp word "quantum jump" of the state after a "filtering intervention" as in our example here) there is no tension between causality and relativistic QFT whatsoever, and that's so by construction of the QFT, and Peres's argument in the paper is just another very convincing argument for why (at least) the Hamilton density operator has to commute at spacelike separation of the arguments, i.e., if $(x-y) \cdot (x-y)<0$ (west-coast convention of the metric) you must have $[\hat{\mathcal{H}}(x),\hat{\mathcal{H}}(y)]=0$. Usually one assumes even more, i.e., that any two local operators commute at spacelike separation of their arguments.

Well, whatever it is you need the mathematics, and it is true that the state is assigned to spacelike surface, and the "update" takes place instantaneously on that surface.

 

[zonde]

I don't know, what you mean by measuring A's photon at different angle.

Let's say A measured her photon with polarizer at an angle $\alpha_1$. B measured his photon at an angle $\beta_1$ and got result "+".
Now what it means to say that "it's totally irrelevant for B what A does with her photon"?
I propose such meaning: if A would have measured her photon with polarizer at an angle $\alpha_2$ then B measuring his photon at the same angle $\beta_1$ could still get result "+".

Or do you have on mind different meaning for "it's totally irrelevant for B what A does with her photon"?

 

[Demystifier]

But that interpretation contradicts the locality of the interaction between A's photon and her polarization measurement apparatus.

But according to the minimal ensemble interpretation (MEI), quantum theory says nothing about the interaction between an individual photon and an individual apparatus. It only talks about a large ensemble of interacting photon-apparatus pairs. At the level of ensemble the interactions are local, but there is no guarantee that interactions are local even at the individual level. It could be that individual interactions contain a non-local part, but that these non-local parts cancel-up in the average at the ensemble level. This is a logical possibility that does not contradict known facts about quantum theory (including relativistic QFT) in the MEI form.

 

[Ken G]

It seems to me that "holistic" and "nonlocal" might mean the same thing, here.

I think there's an important difference. "Nonlocal" still implies an influence of sorts, merely one that is not constrained by the speed of light. "Holistic" takes the mathematics at face value-- the system is a single entity, not made of parts that "influence" each other. If there are not parts, there is not any issue with propagation of influences, either slower or faster than c. One simply rejects the concept of a part influencing another part, and poof, nothing "nonlocal" there, it's just a single thing. That's what the mathematics is, after all-- a single thing, with all the correlations built in.

By the way, the simplest way to think of the state as a "single thing" is to treat it as information, rather than a physical entity. One can imagine there is a physical entity out there if one likes, but that's not what the scientist deals in, the scientist deals in information and using information to make and test predictions. We all create a sense of something "physical" during that process, of course, but we needn't mistake our intuitive imaginings for any part of what we are actually doing when we carry out a test. Above all, we don't tell the mathematical entities we manipulate that they must be subservient to our intuitive pictures-- we must train our intuition to the mathematics that works, not the other way around.

 

[stevendaryl]

I think there's an important difference. "Nonlocal" still implies an influence of sorts, merely one that is not constrained by the speed of light.

I think that nonlocal doesn't necessarily imply FTL influences. Local to me means that the most complete description of the universe "factors" into descriptions of small regions of spacetime, and that the evolution of one region depends only on what's true in neighboring regions. Quantum mechanics is not local in this sense, because in the case of distant entangled systems, the most complete description of the universe does not factor into a bunch of local descriptions. For example, in EPR for photons, the most complete description for Alice's photon is that for any orientation of a polarizing filter, the photon has a 50% chance of passing through that filter. The most complete description for Bob's photon is the same. But the most complete description for Alice, together with the most complete description for Bob doesn't add up to the most complete description for the Alice/Bob system, since it doesn't include the perfect correlation between their results when their filters are aligned.

Classical probabilities can be nonlocal in this sense, as well, but in that case, there is a more complete description that is local.

 

[Ken G]

Let me add to my previous point about the difference between "nonlocal" and "holistic." A lot is made of entanglement as being "spooky", but for some reason I never hear the term "spooky" in the context of the Pauli exclusion principle. Why not? Is not the PEP just as "nonlocal" as EPR? For example, we have stellar remnants the size of planet Earth called "white dwarfs" which can cool to the point that they are completely degenerate, in principle. By then, the star is still the size of Earth, it contains some 10⁵⁷ electrons, and each of those electrons has some ghastly kinetic energy equivalent to a billion Kelvin if they weren't degenerate. Yet with all those electrons zinging around with all that kinetic energy, not a single collision is allowed to occur, and not a single photon is allowed to be emitted (in the idealized limit). Talk about entanglement! The identical nature of those Fermions is such that if you think that is a "system of parts" that are "nonlocally influencing" each other, each electron must be influenced by all the others so that it can "know" it is not allowed to enter a previously occupied state-- across an object the size of Earth. Why isn't that "spooky action at a distance"? If one wants EPR to be a "nonlocal influence," then a black dwarf is the mother of all nonlocal influences. To me, it just makes more sense to think a black dwarf is all one thing, and the information we have about that thing tells us it cannot emit light-- without any "parts" talking to any other "parts." It just isn't made of parts any more, our naive notion that matter is "made of particles" breaks down when the particles are identical and degenerate. One can imagine that a proton is "made of quarks and virtual gluons", but what sense does it make to say something is made of virtual things? We should just accept that our concept of what it means to be "comprised of" tiny pieces is simply not a general description of reality that should work in all situations.

 

[stevendaryl]

Let me add to my previous point about the difference between "nonlocal" and "holistic." A lot is made of entanglement as being "spooky", but for some reason I never hear the term "spooky" in the context of the Pauli exclusion principle. Why not? Is not the PEP just as "nonlocal" as EPR?

I think that they're very closely related. The nonlocality of EPR is due to having nonfactorable composite wave functions, and the Pauli exclusion principle is a constraint on such wave functions.

 

[Ken G]

I think that nonlocal doesn't necessarily imply FTL influences. Local to me means that the most complete description of the universe "factors" into descriptions of small regions of spacetime, and that the evolution of one region depends only on what's true in neighboring regions. Quantum mechanics is not local in this sense, because in the case of distant entangled systems, the most complete description of the universe does not factor into a bunch of local descriptions.

I agree that you are using "nonlocal" in the way I mean "holistic," and that's probably because you are not buying off on the idea that nonlocality must be enforced by "influences" that happen "instantaneously" in an EPR setup. But for those who do wish to maintain a sense of fractured locality, a "pieceness" or "discreteness" to systems that are cobbled together from smaller entities plus influences between those entities, they need a concept of "nonlocal" that does not violate their "discreteness" concept. It's for them that a distinction between nonlocal and holistic must be made.

In other words, to me "holistic" differs from "nonlocal" in the sense that when the ancient Greeks wondered if matter was continuous or comprised of discrete "atoms", they left out a third possibility: it could be analyzed in terms of discrete bits in some situations, continuous fluids in others, and still in others, it could not be thought of either as discrete local bits-and-influences, nor as a continuum maintained by either propagating or nonlocal influences, but instead, a system could be all one thing. I don't think they even imagined that possibility, so how amazing is it that we have come to it with the mathematics of quantum mechanics-- we should embrace that fascinating new possibility, rather than fight it because it is outside our expectations.

For example, in EPR for photons, the most complete description for Alice's photon is that for any orientation of a polarizing filter, the photon has a 50% chance of passing through that filter. The most complete description for Bob's photon is the same. But the most complete description for Alice, together with the most complete description for Bob doesn't add up to the most complete description for the Alice/Bob system, since it doesn't include the perfect correlation between their results when their filters are aligned.

Yes exactly, but notice the significance of how you've built up this scenario-- the "merging" that happened to create the holistic system was a merging of Alice's and Bob's information, more so than a merging of their photons. They don't even possesses their own photons, any more than a white dwarf possesses separate distinguishable electrons. What is holistic is the information, when we treat it together, or about individual photons, when we treat it that way. The system is happening at the level of how we are treating the information, not the sum of two individual electrons and their experimental outcomes. A photon doesn't own its own experimental outcome, a scientist owns that.

 

[Nugatory]

But Gell-Mann said: "People say loosely ,crudely, wrongly that when you measure one of the photons it does something to the other one. It doesn't."
He's not agnostic. He's strongly denying any causative link.

I'm not sure that's a fair assessment of Gell-Mann's claim, because it's not clear exactly what's being denied when we're dealing with a denial of something that has been stated "loosely, crudely". Or as Bhobba said:

Yes - but its for a lay audience. I think a bit of latitude is reasonable.

 

[A. Neumaier]

it is true that the state is assigned to spacelike surface, and the "update" takes place instantaneously on that surface.

No. This is a noncovariant, observer-specific view.
See https://www.physicsforums.com/threads/states-in-relativistic-quantum-field-theory.885079/